Question 120099
Let l= length of rectangle
Then width (w)=2l-5

Area(a) of a rectangle=length(l) * width(w) so we have:
3=l(2l-5) get rid of parens

3=2l^2-5l  subtract 3 from both sides

2l^2-5l-3=0  quadratic in standard form and it can be factored:

(2l+1)(l-3)=0
2l+1=0
l=-1/2------------------no good ---lengths are positive
and
l-3=0
l=3ft-------------length of rectangle
w=2l-5=2*3-5=1ft-----width of rectangle

CK
A=l*w
3=3*1
3=3

Let x=the positive number
x^2-5=five less than the square of the positive#

5x+1=one more than five times the number

so we have:

x^2-5=5x+1  subtract 5x and also 1 from both sides

x^2-5-5x-1=5x+1-5x-1  collect like terms

x^2-5x-6=0  quadratic in standard form and it can be factored:

(x-6)(x+1)=0
x-6=0
x=6-------------------------the positive number
and
x+1=0
x=-1------------------negative number---disregard
x
CK

x^2-5=5x+1
6^2-5=5*6+1

36-5=30+1
31=31


Hope this helps---ptaylor